document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1145205>Question 1145205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Interior and exterior walls of 80,000 square foot rectangular warehouse cost $90 per running foot. The warehouse is to be divided into 10 rooms by four interior walls running in the x direction and one running in the y direction.\r<BR>\n" );
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document.write( "a)	What dimension will lead to minimal total wall cost?<BR>\n" );
document.write( "b)	What is this minimal cost?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #766624 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=766624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let x be the width (in feet) and y the length.  Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy+=+80000 ALIGN=MIDDLE  ALT=\"xy+=+80000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Counting interior and exterior walls, there are 12 walls in the x direction and 6 in the y direction.  The number of linear feet of the walls is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2B6y ALIGN=MIDDLE  ALT=\"12x%2B6y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We need to minimize the cost of the walls, which means minimizing the number of linear feet of the walls.<br><BR>\n" );
document.write( "(1) Express the number of linear feet of walls as a function of a single variable:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+80000%2Fx ALIGN=MIDDLE  ALT=\"y+=+80000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%28x%29+=+12x%2B6%2880000%2Fx%29+=+12x%2B480000%2Fx ALIGN=MIDDLE  ALT=\"L%28x%29+=+12x%2B6%2880000%2Fx%29+=+12x%2B480000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) Find where the derivative of the function is equal to zero.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dL%2Fdx+=+12-480000%2Fx%5E2+=+0 ALIGN=MIDDLE  ALT=\"dL%2Fdx+=+12-480000%2Fx%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+=+480000%2Fx%5E2 ALIGN=MIDDLE  ALT=\"12+=+480000%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2+=+480000 ALIGN=MIDDLE  ALT=\"12x%5E2+=+480000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+40000 ALIGN=MIDDLE  ALT=\"x%5E2+=+40000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+200 ALIGN=MIDDLE  ALT=\"x+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The total number of linear feet, and therefore the total cost of the walls, is minimum when the width is x=200 feet and the length is 80,000/x = 400 feet.<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "(a) width 200 feet, length 400 feet<BR>\n" );
document.write( "(b) (12(200)+6(400))*$90 = (4800)*$90 = $432,000 </SPAN>\n" );
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